"the equation of a parabola in "color(blue)"vertex form" is.
color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))
"where "(h,k)" are the coordinates of the vertex and a"
"is a multiplier"
y=-2(x-1)^2+3" is in vertex form"
"with "h=1" and "k=3
rArrcolor(magenta)"vertex "=(1,3)
"to find the intercepts"
• " let x = 0, in the equation for y-intercept"
• " let y= 0, in the equation for x-intercepts"
x=0rArry=-2(-1)^2+3=1larrcolor(red)"y-intercept"
y=0rArr-2(x-1)^2+3=0
"subtract 3 from both sides"
rArr-2(x-1)^2=-3
"divide both sides by "-2
rArr(x-1)^2=3/2
color(blue)"take the square root of both sides"
sqrt((x-1)^2)=+-sqrt(3/2)larrcolor(blue)"note plus or minus"
rArrx-1=+-sqrt3/sqrt2=+-1/2sqrt6
"add 1 to both sides"
rArrx=1+-1/2sqrt6larrcolor(red)"exact solutions"
x~~-0.22" to 2 dec. places ",x~~2.22larrcolor(red)"x-intercepts"
